Symmetric sums of squares

We consider the problem of finding sum of squares (sos) expressions to establish the non-negativity of a symmetric polynomial over a discrete hypercube whose coordinates are indexed by /(k/)-element subsets of /([n]/). We develop a variant of the Gatermann-Parrilo symmetry-reduction method tailored to our setting that allows for several simplifications and a connection to Razborov's flag algebras. We show that every symmetric polynomial that has a sos expression of a fixed degree also has a succinct sos expression whose size depends only on the degree and not on the number of variables. This is joint work with James Saunderson, Mohit Singh and Rekha Thomas.

GERAD seminar

Aug 31, 2016 03:45 PM
–
05:00 PM

GERAD

GERAD is a multi university research center founded in 1979, financed by FRQNT.
It involves some seventy experts from a mix of disciplines: quantitative methods for management, operations researchers, computer scientists, mathematicians and mathematical engineers, from HEC Montréal, Polytechnique Montréal, McGill University and Université du Québec à Montréal.